Inverse function

$$\phi^{-1}(y) = \frac{1}{9}y^{3}$$ $$\downarrow$$ $$\phi(x) = 9x^{\frac{1}{3}}$$

#!/usr/bin/python
import numpy as np
import matplotlib.pyplot as plot
N = 10000
X0 = np.random.rand(N)
X1 = 3*X0
Y = np.power(9*X1, 1.0/3)
t = np.arange(0.0, 3.0, 0.01)
y = t*t/9
plot.plot(t, y, 'r-', linewidth=1)
plot.hist(Y, bins=50, normed=1, facecolor='green', alpha=0.75)
plot.show()